Abstract

We investigate the issue of aggregativity in fair division problems from the perspective of cooperative game theory and Broomean theories of fairness. Paseau and Saunders (Utilitas 27:460–469, 2015) proved that no non-trivial theory of fairness can be aggregative and conclude that theories of fairness are therefore problematic, or at least incomplete. We observe that there are theories of fairness, particularly those that are based on cooperative game theory, that do not face the problem of non-aggregativity. We use this observation to argue that the universal claim that no non-trivial theory of fairness can guarantee aggregativity is false. Paseau and Saunders’s mistaken assertion can be understood as arising from a neglect of the (cooperative) games approach to fair division. Our treatment has two further pay-offs: for one, we give an accessible introduction to the (cooperative) games approach to fair division, whose significance has hitherto not been appreciated by philosophers working on fairness. For another, our discussion explores the issue of aggregativity in fair division problems in a comprehensive fashion.

Highlights

  • When our collective needs exceed the resources available, or when what is there is less than what is demanded, a fair division problem arises: how, in order to be fair, should a scarce good be divided? Take, for instance, the following fair division problem.Problem I John owes £80 to Ann and £40 to Bob but has only £60 left.How in order to be fair, must John divide the £60 that he has left between Ann and Bob? A popular answer, advocated for by John Broome (1990), is that John must divide the £60 proportional to the claims of Ann and Bob

  • We discussed the claims and games approach to fair division and explained that these approaches harbour theories of fairness that act on different fairness structures

  • We explained that whereas there are no aggregative theories of fairness on the claims approach, there are such theories on the games approach

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Summary

Introduction

When our collective needs exceed the resources available, or when what is there is less than what is demanded, a fair division problem arises: how, in order to be fair, should a scarce good be divided? Take, for instance, the following fair division problem. In a recent paper, Paseau and Saunders (2015) have argued that the aggregated allocation (70, 80) that results from applying the proportional rule to the above two problems is unfair. In a nutshell, their argument runs as follows. 4.1 we revisit Problem I and II both in terms of the RTB rule and the Shapley value and explain that certain conclusions with respect to these problems are an artefact from adopting the claims approach to fair division.

The Claims Approach and Aggregativity
A First Look at the Games Approach
Fairness
The Shapley Value and the Failure of NAT
Aggregativity After the Failure of NAT
Aggregativity in the Claims and Games Approach
The Run-to-the-Bank Rule
How the RTB Rule and Shapley Value Coincide
No Paradox of Aggregativity
What Now for Aggregativity in Fair Division?
Aggregativity on Different Fairness Structures
On the Problem of Non-aggregativity
Aggregativity and the Trade-Off Between Claims and Games
Concluding Remarks
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